Synthesizing robust domains of attraction for state-constrained perturbed polynomial systems

In this paper we propose a novel semidefinite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory starting from it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. The semidefinite program is constructed by relaxing a generalized Zubov's equation. The existence of solutions to the constructed semidefinite program is guaranteed, and there exists a sequence of solutions such that their strict one-sublevel sets inner-approximate the interior of the maximal robust domain of attraction in measure under appropriate assumptions. Some illustrative examples demonstrate the performance of our method.